Spherical bessel functunction help

[lycraa]

Homework Statement

i need to derive the recurrence relations for the spherical Bessel function. i got j_n-1(x)+j_n+1(x)=(2n+1)/x j_n(x) but i can't get nj_n-1(x)-(n+1)j_n+1(x)=(2n+1) j'_n(x). i know i have to use j_n(x)=(pi/2x)^1/2J_n+1/2(x) and the recurrence relations for regular bessel functions J_n-1(x)-J_n+1(x)=2 J'_n(x) and possibly also J_n-1(x)+J_n+1(x)=2n/x J_n(x). i don't even know were to start because i don't know were the 'n's come from in the recurrence relation I'm trying to derive.

Homework Equations

above

The Attempt at a Solution

i just need to know were to start! nothing I've tried comes even close

 

[fzero]

Start by computing $$j_n'(x)$$ in terms of $$J_{n+1/2}(x)$$. Use the ordinary recurrence relation to eliminate $$J'_{n+1/2}(x)$$.